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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Indirect Waves (I-Waves)

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Dr. Rishabh Pathak

Indirect Waves (I-Waves) are a concept in the field of transcranial magnetic stimulation (TMS) that play a crucial role in understanding the mechanisms of cortical activation and neural responses to magnetic stimulation. Here is an overview of Indirect Waves (I-Waves) and their significance in TMS research:


1.      Definition:

o Indirect Waves (I-Waves) refer to neural responses evoked by transcranial magnetic stimulation that are believed to result from the activation of interneurons in the cortex rather than direct activation of pyramidal neurons.

2.     Mechanism:

o  When a magnetic pulse is applied to the motor cortex using TMS, it can lead to the generation of different types of waves in the corticospinal pathway.

o Indirect Waves (I-Waves) are thought to represent the indirect activation of cortical interneurons, particularly in layer II and III, which then influence the excitability of pyramidal neurons in layer V.

3.     Generation:

o    I-Waves are generated through a complex interaction of the magnetic field with neural elements in the cortex, leading to the recruitment of interneurons and the propagation of neural activity along cortical circuits.

o  These waves are believed to contribute to the modulation of cortical excitability and the generation of motor responses following TMS.

4.    Role in Cortical Activation:

o  I-Waves are essential for understanding the mechanisms of cortical activation and the spread of neural activity following TMS.

o    They are part of the cascade of neural events that occur in response to magnetic stimulation and contribute to the overall effect on motor output and cortical plasticity.

5.     Relationship to Direct Waves (D-Waves):

o  In contrast to Indirect Waves (I-Waves), Direct Waves (D-Waves) are thought to result from the direct activation of pyramidal neurons, particularly in layer V, by the magnetic field generated during TMS.

o  The interplay between I-Waves and D-Waves provides insights into the complex neural dynamics underlying TMS-induced cortical responses.

6.    Research Significance:

o  Studying Indirect Waves (I-Waves) is important for elucidating the neural mechanisms of TMS effects on cortical circuits, motor function, and plasticity.

o By investigating the characteristics and modulation of I-Waves, researchers can gain a deeper understanding of how TMS influences neural activity and connectivity in the brain.

In summary, Indirect Waves (I-Waves) represent a key aspect of neural responses to transcranial magnetic stimulation, reflecting the activation of interneurons and the propagation of neural activity in cortical circuits. Understanding the role of I-Waves is essential for unraveling the complex mechanisms of TMS-induced cortical activation and its implications for brain function and plasticity.

 

 

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